Certificate for #5822 ⟨a, b, c | ab=a, aca=cc⟩

Back:⟨a, b, c | ab=a, aca=cc⟩

Completion settings:

[1] ab=a

Axiom: ab=a.

Defines rule #1.

Referenced by [3].

[2] aca=cc

Axiom: aca=cc.

Defines rule #2.

Referenced by [3], [4].

[3] ccb=cc

Overlap of [2] aca=cc with [1] ab=a:

ac a ab

Critical pair: aca=ccb.

Reduce LHS:

[2](aca)
⇒ cc

Flip LHS and RHS.

Defines rule #3.

[4] ccca=accc

Overlap of [2] aca=cc with [2] aca=cc:

ac a aca

Critical pair: accc=ccca.

Flip LHS and RHS.

Defines rule #4.